Lattices of intermediate subfactors for type III factors

Tamotsu Teruya, Yasuo Watatani

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Abstract

Let M be a factor and N a subfactor of M with finite index. If N is an irreducible subfactor of M, then the intermediate subfactor lattice for the inclusion N ⊂ M is a finite lattice. In a common discrete decomposition intermediate subfactor lattices of type II and type III inclusions are different in general. But they are isomorphic in a common continuous decomposition of a type III1 inclusion. We determine the structure of lattices of subfactors with index 4 without the assumption of AFD.

Original languageEnglish
Pages (from-to)454-463
Number of pages10
JournalArchiv der Mathematik
Volume68
Issue number6
DOIs
Publication statusPublished - Jun 2 1997

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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